Superheating fields of semi-infinite superconductors and layered superconductors in the diffusive limit: Structural optimization based on the microscopic theory

Abstract

The superheating field Hsh of the Meissner state is thought to determine the theoretical field-limit of superconducting accelerator cavities. We investigate Hsh of semi-infinite superconductors and layered structures in the diffusive limit using the well-established quasiclassical Green's function formalism of the BCS theory. The coupled Maxwell-Usadel equations are self-consistently solved to obtain the spatial distributions of the magnetic field, screening current density, penetration depth, pair potential, and Hsh. For a semi-infinite superconductor in the diffusive limit, we obtain Hsh = 0.795 Hc0 at the temperature T →0. Here, Hc0 is the thermodynamic critical-field at the zero temperature. By laminating a superconducting film (S) with the thickness d on a semi-infinite superconductor (Σ), we can engineer Hsh (d) of the layered structure. When d is the optimum thickness d, Hsh can be larger than that of the simple semi-infinite superconductors made from the S and Σ materials: Hsh (dm) > max {Hsh(S), Hsh (Σ)}. The present study addresses the calculation of Hsh of the dirty heterostructure using the microscopic theory from beginning to end for the first time, which contributes to the microscopic understanding of the surface engineering for pushing up the accelerating gradient of superconducting cavities for particle accelerators.